Concept
Basics of visualization is pure geometrics .
In the 1.step it's calculated, how the angle between the direction from earth to sun is changing according to inclination of the axis of the earth depending on dato. The result gives a vector connecting the centres of earth and sun.
In the 2. step this vector is used as normalvector of a plane E containing centre of the earth. E divides earth in two parts representing day and night. For each circle of latitude bg the ratio between archlength lieing in daypart and length of circle is exactly the same as the percentage of daylength from 24 h.
In the 3. step we follow an observer Bg rotating on its circle of latitude togehter with earth, From the postionvector from geocenter to Bg and the normalvector of E at every time the angle between ray of sunlight and horizon is calculated.